What is the Greatest Common Factor of 1582 and 1588?

Greatest common factor (GCF) of 1582 and 1588 is 2.

GCF(1582,1588) = 2

We will now calculate the prime factors of 1582 and 1588, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1582 and 1588.

How to find the GCF of 1582 and 1588?

We will first find the prime factorization of 1582 and 1588. After we will calculate the factors of 1582 and 1588 and find the biggest common factor number .

Step-1: Prime Factorization of 1582

Prime factors of 1582 are 2, 7, 113. Prime factorization of 1582 in exponential form is:

1582 = 2¹ × 7¹ × 113¹

Step-2: Prime Factorization of 1588

Prime factors of 1588 are 2, 397. Prime factorization of 1588 in exponential form is:

1588 = 2² × 397¹

Step-3: Factors of 1582

List of positive integer factors of 1582 that divides 1582 without a remainder.

1, 2, 7, 14, 113, 226, 791

Step-4: Factors of 1588

List of positive integer factors of 1588 that divides 1582 without a remainder.

1, 2, 4, 397, 794

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1582 and 1588. The biggest common factor number is the GCF number.
So the greatest common factor 1582 and 1588 is 2.

Also check out the Least Common Multiple of 1582 and 1588